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The study investigates the transient dynamics of a third-grade fluid, capable of undergoing exothermic reactions, in a two-dimensional rectangular micro-channel. The combined effects of the adverse pressure gradients and electro-osmotic forces constitute the primary flow drivers. In addition to exothermic reactions, the system if also subjected to joule heating and convective cooling at the micro-channel boundaries. Newton's law of cooling and Arrhenius kinetics are employed to model the boundary-cooling and exothermic-reactions respectively. The temperature-dependent fluid viscosity is modelled via a Nahme-type law. It is assumed that the area in between the micro-channels is a porous material with constant permeability. Computational solutions (implemented on the MATLAB software) are employed for the non-homogeneous partial differential equations for temperature and velocity. These computational solutions are developed from efficient, convergent, and unconditionally stable, semi-implicit finite difference methods. In contrast, the linearized Poisson–Boltzmann equation is solved analytically. The sensitivity of the field variables to variations in the various flow parameters are explored graphically and discussed qualitatively. [ABSTRACT FROM AUTHOR]

Entropy generation analysis combined with hybrid nanofluid flow principles contribute to the development of more efficient drug delivery systems for cancer treatment. By using nanofluids, it is possible to improve the transport and targeted release of therapeutic agents to specific sites in the body, allowing for better control and efficiency in treating cancerous cells. Keeping these important applications in view, in the current analysis, the production of irreversibility and stagnant point hybrid nanofluid flow has been considered on a Riga plate. The impacts of nonlinear convection and solar radiations have also been used in this study. Glycol (C3H8O2) is taken as base fluid, while nanoparticles of copper (Cu) and aluminum oxide (Al2O3) have been mixed in it to obtain a hybrid nanofluid. The leading equations for the study have converted to dimensionless form by employing a set of suitable variables and then have been solved by using an artificial neural network (ANN). In order to evaluate the effectiveness of the least mean square neural network algorithm (LMS-NNA), statistical neural network techniques are employed, encompassing error analysis and curve-fitting graphs. It has been revealed in this work that an upsurge in EMHD Riga plate factor and the Grashof number escalates the velocity distribution for both nanoparticles as well as hybrid nanoparticles and is opposed by augmentation in width factor for electrode/magnet. The increase in the nanoparticle volume fraction from 0.01 to 0.05 escalates the heat transfer rate up to 7.6% in the case of nanofluid with Cu-nanoparticles while this increase is 9.3% using hybrid nanofluid Cu + Al2O3. These results show that HNF are more efficient in improving the HT rate. [ABSTRACT FROM AUTHOR]

Low-carbon steel (AISI 1010) is the predominant material used in industrial food processing equipment. Such equipment is vulnerable to the corrosive environment produced by various production stages. Different processes, such as sulphonation and carbonation, are used in the processing of sugar in the sugar industry, creating a corrosive atmosphere. The corrosion behavior of low carbon steel (AISI 1010) is strongly influenced by grain size variations, which in turn affect the microstructural mechanical properties of the material. The mechanical behavior and performance of metallic materials, including their corrosion resistance, is determined by grain size which is an important parameter for this phenomena. The impact of low-carbon steel (AISI 1010) microstructure on corrosion behavior is discussed in this work. Heat treatment produces two different types of microstructure from the same material, which are then analyzed. Scanning Electron Microscopy (SEM) and Energy Dispersive Spectroscopy (EDS) have both been used to study characteristics including morphology and content. By supplying an appropriate corrosive medium, the corrosion performance of several microstructures of low-carbon steel (AISI 1010) was assessed, and corrosion rates were calculated using weight-loss and electrochemical techniques. Results show that the creation of a protective coating with a higher charge transfer resistance is caused by the adsorption process. The variety in phases and grain sizes may contribute to the corrosion stability of different microstructures, and as a result, the corrosion rate lowers as average grain sizes are reduced. Employing the galvanic effect, pearlite increases the rate of ferrite corrosion. The study's findings support the notion that quenching low-carbon steel (AISI 1010) results in a finer grain structure and greater corrosion resistance. [ABSTRACT FROM AUTHOR]

Among various non-Newtonian models, the current study considers Maxwell fluid flow between cone and disk devices in conjunction with dual diffusion. In this scenario, the combination of Fourier's and Fick's law assumptions, including the Cattaneo–Christov heat and mass flux terminologies, is used for describing heat and mass transfer, respectively. The flow is analyzed in four different cases including: (i) rotation of the disk and cone in the reverse direction, (ii) rotation of both cone and disk in one direction, (iii) rotation of the cone and stationary status of the disk, and (iv) rotating disk with the stationary cone. The primary governing model consists of partial differential equations, which are tackled through the control volume finite element method (CVFEM). This system is reduced into a set of nonlinear ordinary differential equations with the help of similarity variables, which is solved using the Runge–Kutta fourth-order (RK-4) technique. In order to understand heat transfer and mass diffusion, the performance of the physical parameters is analyzed for the potential applications of heat exchange devices. It is observed that the increasing Maxwell parameter has inauspicious effects on fluid motion and thermal state. The radial component of velocity is noted to dwindle with higher magnetic parameter. Meanwhile, the case of a swirling disk and a still cone improves the transverse velocity. Despite that, the thermal boundary layer is observed to be an increasing function of thermophoretic and Brownian motion parameters. Moreover, higher thermal relaxation time and Prandtl number fasten the convection process. Furthermore, the thermophoretic parameter, concentration relaxation parameter, and Schmidt number have apparently favorable effects on relative mass diffusion regions compared to the Brownian parameter. [ABSTRACT FROM AUTHOR]

The flow at a time-independent separable stagnation point on a Riga plate under thermal radiation and electro-magnetohydrodynamic settings is examined in this research. Two distinct base fluids-H2O and C2H6O2 and TiO2 nanostructures develop the nanocomposites. The flow problem incorporates the equations of motion and energy along with a unique model for viscosity and thermal conductivity. Similarity components are then used to reduce these model problem calculations. The Runge Kutta (RK-4) function yields the simulation result, which is displayed in graphical and tabular form. For both involved base fluid theories, the nanofluids flow and thermal profiles relating to the relevant aspects are computed and analyzed. According to the findings of this research, the C2H6O2 model heat exchange rate is significantly higher than the H2O model. As the volume percentage of nanoparticles rises, the velocity field degrades while the temperature distribution improves. Moreover, for greater acceleration parameters, TiO2/ C2H6O2has the highest thermal coefficient whereas TiO2/ H2O has the highest skin friction coefficient. The key observation is that C2H6O2 base nanofluid has a little higher performance than H2O nanofluid. [ABSTRACT FROM AUTHOR]

This study looks at the natural convections of Cu + Al2O3/H2O nanofluid into a permeable chamber. The magnetic field is also executed on the flow field and the analysis has been approached numerically by the control volume method. The study of hybrid nanofluid heat in terms of the transfer flux was supplemented with a wide range of parameters of hybrid nanofluid fractions, Rayleigh numbers Hartmann numbers and porosity factor. It's also determined that the flow and thermal distribution are heavily affected by the concentration of the nanoparticles. The concentration of nanoparticles increases the transport of convective energy inside the enclosure. The primary findings demonstrate that a rise in both the Rayleigh number and Darcy number leads to an improvement in convective heat transfer within the enclosure. However, the porosity has a negligible effect. Additionally, the rotation in a clockwise direction has a beneficial impact on the dispersion of heat transfer throughout the cavity. Furthermore, it is concluded that hybrid nanofluids are more reliable than conventional fluids in improving thermal properties. [ABSTRACT FROM AUTHOR]

This investigation describes the hydromagnetic flow of gravity-driven couple stress hybrid nanofluid past a heated plate. The carbon nanotubes (CNTs) are used to characterize the hybrid nanofluid. The heated plate is placed vertically with an application of homogenous-heterogeneous reactions to the assumed flow system. The homogeneous reaction governs by isothermal cubic autocatalytic kinetics while the heterogeneous reaction governs by the first order kinetics. For current study the couple stress hybrid nanofluid is presumed to be conducted electrically with impact of non-uniform magnetic effects. An appropriate set of dimensionless quantities has employed to governing equations and then has solved by homotopy analysis method. The influence of emerging parameters encountered in this work has discussed in detail with the help of graphs. In this study it has examined that, flow of fluid reduces with upsurge in magnetic parameter and volumetric concentrations, whereas thermal and concentration characteristics augment with increase in volumetric concentrations. Moreover, growth in Prandtl number leads to a reduction in thermal characteristics and growth in Schmidt number result a reduction in concentration profile. The impact of various emerging parameters has also studied numerically upon physical quantities. It has established that, with augmentation in values of buoyancy parameter there is a growth in the values of skin friction. A comparison has also carried out between current and established results with a fine agreement in both results. [ABSTRACT FROM AUTHOR]

In this work, the thermal analysis for bio-convective hybrid nanofluid flowing upon a thin horizontally moving needle is carried out. The chemical reaction and viscous dissipation has also considered for flow system in the presence of microorganism. The hybrid nanoparticles comprising of Copper Cu and Alumina A l 2 O 3 are considered for current flow problem. Mathematically the flow problem is formulated by employing the famous Buongiorno's model that will also investigate the consequences of thermophoretic forces and Brownian motion upon flow system. Group of similar variables is used to transform the model equations into dimensionless form and have then solved analytically by homotopy analysis method (HAM). It has established in this work that, flow of fluid declines due to increase in bioconvection Rayleigh number, buoyancy ratio and volume fractions of nanoparticles. Thermal flow grows due to rise in Eckert number, Brownian, thermophoresis parameters and volume fraction of nanoparticles. Concentration profiles increase due to growth in Brownian motion parameter and reduces due to increase in thermophoresis parameter and Lewis number. Motile microorganism profile declines due to augmentation in Peclet and bioconvection Lewis numbers. Moreover, the percentage enhancement in the drag force and rate of heat transfer using conventional nanofluid and hybrid nanofluid are observed and discussed. The hybrid nanofluid increases the skin friction and heat transfer rate more rapidly and efficiently as compared to other traditional fluids. A comparison of the present study with the existing literature is also conducted with a closed agreement between both results for variations in thickness of the needle. [ABSTRACT FROM AUTHOR]

We analyze the convergence properties of the spectral method when used to approximate smooth solutions of delay differential or integral equations with two or more vanishing delays. It is shown that for the pantograph-type functional equations the spectral methods yield the familiar exponential order of convergence. Various numerical examples are used to illustrate these results. [ABSTRACT FROM AUTHOR]

This paper presents a new numerical approximation method to solve a system of nonlinear Fredholm integral equations of second kind. Spectral collocation method and their properties are applied to determine the general solution procedure for nonlinear Fredholm integral equations (FIEs). The convergence and error analysis of spectral collocation method are incorporated for the given nonlinear model. Legendre–Gauss–Lobatto (LGL) points are used as collocation points with various Legendre–Gauss quadrature with weight functions. The use of Legendre polynomials, together with the Gauss quadrature collocation points is well known for the accurate approximations that converge exponentially. Finally, we validate our theoretical results with a number of numerical examples, which further enhance the efficiency of our proposed scheme. [ABSTRACT FROM AUTHOR]

Volterra integro-differential equations arise in the modeling of natural systems where the past influence the present and future, for example pollution, population growth, mechanical systems and financial market. Furthermore, as many real-world phenomena are subject to perturbations or random noise, it is natural to move from deterministic models to stochastic models. Generally exact solutions of such models are not available and numerical methods are used to obtain the approximate solutions. Therefore the efficiency and long-term behavior of approximate solutions for these systems is an important area of investigation. This paper presents a new numerical approach for the approximate solution of stochastic Volterra integro-differential (SVID) equations based on the Legendre-spectral collocation method. In order to fully use the properties of orthogonal polynomials, we use some function and a variable transformation to change the given SVID equation into a new equation, which is defined on the standard interval [ − 1 , 1 ] . For the evaluation of the integral term efficiently a Legendre–Gauss quadrature formula will be used. A rigorous error analysis of the proposed scheme will be provided under the assumption that the solution of the given SVID is sufficiently smooth. For the illustration of our theoretical results a number of numerical experiments will be performed. [ABSTRACT FROM AUTHOR]

Multi-species models play an important role in both ecology and mathematical ecology due to their practical relevance and universal existence. Some phenomena include but are not limited to osculating solutions behavior, multiple steady states and spatial patterns formation. In this article we study the numerical approximation of Turing patterns corresponding to the steady state solutions of systems of reaction-diffusion equations subject to zero-flux boundary conditions. We apply Chebyshev spectral methods which proved to be numerical methods that can significantly speed up the computation of systems of reaction-diffusion equations in the spatial part, while the temporal part is discretized using the Euler scheme in one dimension. For the evaluation of Turing instabilities and bifurcation of the steady state problem, we used the eigenvalues of the Jacobian matrix. The proposed scheme is then extended to the two-dimensional problem. We found that our numerical scheme is in very good agreement with other schemes available in the literature. [ABSTRACT FROM AUTHOR]